Da Costa worked at the National Treasury Secretariat, working in the Strategic Planning Coordination of Public Debt of the National Treasury and in the Secretariat of Economic Planning of the Ministry of Finance. Since returning to academic life in 2003, Costa has twice served as a board member of the Brazilian Society of Econometrics and is currently associate editor of the Brazilian Journal of Economics. Costa has his work published in important periodicals such as the Journal of Political Economy, Journal of Public Economics, European Economic Review and Review of Dynamic Economics. da Costa acts as a reviewer of the Journal of Political Economy, Review of Economic Studies, Journal of Public Economic Theory, Review of Economic Dynamics, Research in Economics, Brazilian Journal of Economics and Journal of Econometrics. He is currently a board member of the International Institute of Public Finance (IIPF).